Question

If there are two companies who control the market and compete on price what would the payoff matrix look like for the prisoner’s dilemma? DRAW THE MATRIX (Company A on top, B on the side, when both go high the profit $36 for A and $36 for B when both go low the profit is $18 for A and $18 for B, When A goes high and B goes low the profit is $48 for B and $16 for A and when A goes low and B goes high the profit is $16 for B and $48 for A and) What will they end up doing? What does it mean to have a dominant strategy in the prisoner’s dilemma? What is a Nash-equilibrium? Is the solution for this problem Nash?Would you expect the same result if this was a “repeated” game? Explain.

Answer 1

Consider the given problem here there are two companies and both of them have two possible strategies “High Price” and “Low Price”. Consider the following payoff matrix here “B” is a row player and “A” is a column player.

So, here if “B” chooses “High”, => the optimum choice for “A” is “low price”, since under low price “A” will get higher profit that is “48”. Similarly, if “A” chooses “Low”, => the optimum choice for “B” is “low price”, since under low price “B” will get higher profit that is “18”. So, here “Low, Low” be the optimum choice and the game end up here and both the player will get “18, 18” as a payoff.

Here “Low” is the dominant strategy choice of both players. Since under both cases the profit under “Low” is higher for both player, => “Low” is the dominant strategy choice for both players. So, the only solution of the game is “Low, Low” and both will get “18” as a profit.

In this game there is a unique NE, => if the game will be played repeatedly for finite numbers of time, => in the each and every cases there will be only one solution which is “Low, Low”. But if the game will be played for infinite numbers of time then the solution may be differ.